The conormal and Robin boundary value problems in nonsmooth domains satisfying a measure condition

Heat Kernels and Hardy Spaces on Non-Tangentially Accessible Domains with Applications to Global Regularity of Inhomogeneous Dirichlet Problems

“…Meanwhile, it is easy to see that a (γ, R)-Reifenberg flat domain is also a (γ, σ, R) quasi-convex domain for some σ ∈ (0, 1). In recent years, boundary value problems of elliptic or parabolic equations on Reifenberg flat domains have been widely concerned and studied (see, for instance, [8,11,23,24,25]). (ii) It is known that, for any open set Ω ⊂ R n with compact boundary, Ω is a semi-convex domain of R n if and only if Ω is a Lipschitz domain satisfying a uniform exterior ball condition (see, for instance, [48,49,67] for the definitions of both the semi-convex domain and the uniform exterior ball condition).…”

“…The study of elliptic value problems on non-smooth domains of R n has a long history (see, for instance, [21,39,43] and the references therein). In recent years, the research of the global regularity for elliptic equations with rough coefficients on non-smooth domains of R n has aroused great interest (see, for instance, [11,21,22,23,24,25,30,57,59]). The global regularity estimates of elliptic equations with rough coefficients on the non-smooth domain Ω of R n in the scale of Lebesgue spaces L p (Ω), with p ∈ (1, ∞), have been extensively studied in the existing literatures (see, for instance, the recent survey article [21], the monograph [57], and the references therein).…”